Answer to Question #211513 in Algebra for Moe

Question

Let $a(x) =$ $x^3 - 2x - 4$

Which of the following is true?

1. $a(x))$ is not a polynomial
2. The remainder when $a(x)$ is divided by $x + 2$ is 0
3. $a(x)$ is divisible by $x - 2$
4. $a(-1) = 3$
5. None of the above

Answer 1

$a(x))$ is not a polynomial

false because it is a polynomial.

2:

The remainder when a(x) is divided by x+2 is 0

Check

$\frac{x^3-2x-4}{x+2}$

Find the next term of the quotient and the remainder

$x^2+\frac{-2x^2-2x-4}{x+2}$

$\frac{x^3-2x-4}{x+2}$

Find the next term of the quotient and the remainder m

$\frac{x^3-2x-4}{x+2}$

Find the next term of the quotient and the remainder

$x^2-2x+\frac{2x-4}{x+2}$

Find the next term of the quotient and the remainder

$x^2-2x+2+\frac{-8}{x+2}$

Simplify the sign in the fraction

$x^2-2x+2-\frac{8}{x+2}$

False because the remainder is -8.

3: 

a(x) is divisible by x-2

Check

Use polynomial division for x

$\frac{x^3-2x-4)}{x-2}$

Find the next term of the quotient and the remainder

$x^2+\frac{-2x^2-2x-4}{x-2}$

Find the next term of the quotient and the remainder

$x^2+2x+\frac{2x-4}{x-2}$

Find the next term of the quotient and the remainder

$x^2+2x+2$

True because a(x) divide by 2 is $x^2+2x+2$

4:

$a(-1)=3\\check\\a(-1)=(-1)^3-2(-1)-4=-1+2-4=-5+2=-3\\False$